Projectile Motion: Determine v_0 to go over a fence

AI Thread Summary
To determine the initial speed v0 needed to hit a baseball over a fence of height H and distance D, the equations of projectile motion are utilized. The vertical motion equation y = y0 + (v0*sinθ)t - ½gt² is combined with the horizontal motion equation x = v0*t*cosθ to eliminate time t. A user attempted to solve for v0 but ended up with a complex equation, prompting concerns about its accuracy. Suggestions include plotting parametric equations to verify the solution and ensuring the correct interpretation of variables, particularly setting y0 to zero. Simplifying the equations using trigonometric identities may also help in finding a clearer solution.
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Homework Statement


You're the new home run hitter for a baseball team. Your job is to hit the ball over a fence D away and H high. For a given angle θ calculate the speed with which the ball must be hit v0 to go over the top of the fence.

Homework Equations


1. y = y0+(v0*sinθ)-½gt2
2. x = v0*t*cosθ

The Attempt at a Solution



I tried using H as my y value from eq. 1 and D as my x value in eq. 2. I solved for v0 in eq. 2 (D/(t*cosθ)), then attempted to eliminate t by solving for it in equation 1 using the quadratic formula. Then I substituted the result into the D/(t*cosθ) equation.

The result is a very bulky equation that I'm unsure is correct. A tutor said my reasoning was sound, and was unable to come up with a more simplified answer himself. What do you guys think? Am I even on the right track here?
 
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Dr. Courtney said:
it's complicated.

The problem, the answer, or both?
 
The best double check is to plot the resulting parametric equations with real numbers and see if it clears the fence.
 
Your quoted equation for y is missing something. I assume that's just a typo.
I assume H is the height relative to the point of impact, so y0=0.
The only use of t here is to connect the horizontal and vertical motions, so I would start by obtaining a single equation relating x and y, with t absent.
After that it does not look complicated to me. You can get a small simplification by using the formulae for sin(2θ) and cos(2θ).
Please post your working.
 
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